Following a companion paper on analytical methods, this paper presents simulation as a complementary method for analyzing the reliability of water distribution networks. For this simulation, the distribution system is modeled as a network whose pipes and pumps are subject to failure. Nodes are targeted to receive a given supply at a given head. If this head is not attainable, supply at the node is reduced. Pumps and pipes fail randomly, according to probability distributions with userspecified parameters. Several reliability measures are estimated with this simulation. Confidence intervals are also supplied for some of these reliability measures. Simulation results are presented for a small network (ten nodes) and a larger network (sixteen nodes). Simulation enables computation of a much broader class of reliability measures than do analytical methods, but it requires considerably more computer time and its results are less easy to generalize. It is therefore recommended that analytical and simulation methods be used together when assessing the reliability of a system arid considering improvements.

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Probabilistic reliability measures for the performance of water distribution networks are developed and analytical methods for their computation explained. The paper begins with a review of reliability considerations and measures for water supply systems, making use of similar notions in other fields. It classifies reliability analyses according to the level of detail with which the water system is modeled, and then concentrates on methods relevant to networks. Two probabilistic measures, reachability (connection of a specific demand node to at least one source) and connectivity, are explored for use in water distribution systems. Two algorithms for their computation are presented, one for series-parallel networks and one for general networks. These measures are computed for two systems, each with ten nodes. Additionally, the probability that a given point receives sufficient supply is proposed for use as a reliability measure. For the calculation of this measure, an algorithm is provided that combines a capacitated network algorithm with a method to efficiently search through network configurations involving multiple link failures. This measure is calculated for the two sample systems.

A stochastic optimization model for containment of a plume of groundwater contamination through the installation and operation of pumping wells is developed. It considers explicitly uncertainty about hydraulic conductivity in the aquifer and seeks to minimize the expected total cost of operating the pumping wells plus the recourse cost incurred when containment of the contaminant plume is not achieved. Four different formulations of the model are examined, ranging from simply replacing all uncertain parameters by their expected values to a full stochastic programming with recourse model involving nonsymmetric linear quadratic penalty functions. The full stochastic programming with recourse model, which minimizes the expected total costs over a number of realizations of outcomes of the random parameters, is nonlinear and possibly nonconvex and is solved by an extension of the finite generation algorithm. The value of information about the uncertain parameters is defined through the differences between the values of the optimal solutions to the different formulations. A sample problem is solved using all four formulations. The results indicate that the explicit incorporation of uncertainty does make a difference in the solutions obtained. The work indicates that stochastic programming with recourse is a useful tool in management under uncertainty, and that it can be used with reasonable computational resources for problems of moderate size.

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